Coupled electron pair approximation CEPA

Coupled—Pair Functional (ACPF) and Coupled Electron Pair Approximation (CEPA). The simplest form of CEPA, CEPA-0, is also known as Linear Coupled Cluster Doubles (LCCD). 

Besides the mentioned aperiodicity problem the treatment of correlation in the ground state of a polymer presents the most formidable problem. If one has a polymer with completely filled valence and conduction bands, one can Fourier transform the delocalized Bloch orbitals into localized Wannier functions and use these (instead of the MO-s of the polymer units) for a quantum chemical treatment of the short range correlation in a subunit taking only excitations in the subunit or between the reference unit and a few neighbouring units. With the aid of the Wannier functions then one can perform a Moeller-Plesset perturbation theory (PX), or for instance, a coupled electron pair approximation (CEPA) (1 ), or a coupled cluster expansion (19) calculation. The long range correlation then can be approximated with the help of the already mentioned electronic polaron model (11). 

It is now well established by numerous and extensive applications that the single reference (SR) based many-body methods, viz. many-body perturbation theory (PT) [1], coupled cluster (CC) theory [2], coupled electron-pair approximations (CEPA) [3], etc. provide rather accurate descriptions of the energy in and around the equilibrium geometry of the closed-shell states. In particular, the single reference coupled cluster (SRCC)... 

Two ab initio methods, which were well known and much discussed in the 1970s and 1980s, were the pair natural orbital Cl (PNO-CI) method and the coupled electron pair approximation (CEPA) method. They were proposed by Meyer [67] in 1973 and 2 years later improved by Ahlrichs et al. [68]. In 1983, Burton and Senff [69] applied the method of Ahlrichs et al. to an analysis of the anisotropy of (H2)2 interaction near the minimum in the van der Waals interaction energy. 

P.G. Szalay, Towards state-specihc formulation of multireference coupled-cluster theory Coupled electron pair approximations (CEPA) leading to multireference configuration interaction (MR-CI) type equations, in R.J. Bartlett (Ed.), Modem ideas in coupled-cluster methods, World Scientific, Singapore, 1997, pp. 81-123. 

In a study on the proton afrinity of diacetylene, Botschwina et al. reported more extended ab-initio calculations for C4H2 by allowing for effects of electron correlation, using the coupled-electron-pair approximation (CEPA) [207], Thor obtained C —C bond lengths of... 

Numerous ab initio calculations with at least split-valency quality basis sets have been performed. The results are extremely sensitive to the choice of the basis set, especially the inclusion of d orbitals, and to the procedure applied, such as nth-order Moller-Plesset theory (MPn, up to n = 4) [3 to 7], coupled electron pair approximation (CEPA) [1,2, 8, 9], configuration interaction (Cl) [8, 10, 11], or SCF MO calculations [12 to 19]. For semiempirical calculations, see [20, 21 ] (EHMO), [22] (PRDDO, partial retention of diatomic differential overlap), and [23] (INDO, intermediate neglect of differential overlap). 

The coupled electron-pair approximation (CEPA). This starts from the hierarchy of the full Cl equations. A truncation on the SD level is then achieved by approximating the Hamiltonian matrix elements which couple the singles and doubles with higher terms (triples, quadruples). 

In Section 5.2 we consider how to go beyond the lEPA by incorporating coupling between different pairs of electrons. We will discuss the coupled pair many-electron theory (CPMET) which is also called the coupled-cluster approximation (CCA). We then describe a number of simplifications to this rather sophisticated approach in particular, we consider the coupled electron pair approximation (CEPA). Finally, in Subsection 5.2.4 we present some numerical applications of coupled-pair theories. 

Linear CCA and the Coupled-Electron Pair Approximation (CEPA)... 

We now consider a different approximation to CCA, originally proposed and implemented by W. Meyer called the Coupled Electron Pair Approximation (CEPA). We begin again with the CCA equation (5.55). Instead of ignoring all the terms involving we retain those where c = a and Thus we have... 

---